Uncertainty expressed in this answer

I'm trying to figure out the correct way to calculate and express the uncertainty for this equation:
1/(-1730 ± 1.1)
I need to get something like -5.780 ± something

1/(-1730 ± 1.1) = 1/(-1730 ∓ 1.1)

= (-1730 ± 1.1)/((-1730 ∓ 1.1)(-1730 ± 1.1))

= (-1730 ± 1.1)/((-1730)²-(1.1)²)

= (-1730 ± 1.1)/2992898.79

= -1730/2992898.79 ± 1.1/2992898.79

= -0.0005780349 ± 0.0000003675

= (-5.780349 ± 0.003675) * 10⁻⁴


Mαthmφm